NATIONAL UNIVERSITY OF SINGAPORE

Department of Mechanical Engineering

ME2135 Fluid Mechanics IIPart 2 External Incompressible Viscous FlowTutorial 11. The average pressure and shear stress acting on the surface of the 1-msquare flat plate are as indicated in Fig. 1. Determine the lift and draggenerated. Determine the lift and drag if the shear stress is neglected.Compare these two sets of results.

Fig. 1 Flow past an inclined flat plate; from [1]

Copyright National University of Singapore

2. An atmospheric boundary layer is formed when the wind blows over

the earths surface. Typically, such velocity profiles can be written as apower law: u = ayn, where the constants a and n depend on theroughness of the terrain. As is indicated in Fig. 2, typical values are n =0.40 for urban areas, n = 0.28 for woodland or suburban areas, and n =0.16 for flat open country. (a) If the velocity is 6 m/s at the bottom of thesail on your boat (y = 1.2 m), what is the velocity at the top of the mast (y= 9 m)? (b) If the average velocity is 16 km/h on the tenth floor of anurban building, what is the average velocity on the sixtieth floor?

Fig. 2 Atmospheric boundary layer flow over different terrains; from [1]Copyright National University of Singapore

3. The velocity profile in a laminar boundary layer is approximated by a

(continuity with freestream)

4. Air enters a square duct through a 0.3 m opening as is shown in Fig. 4.

Because the boundary layer displacement thickness increases in thedirection of flow, it is necessary to increase the cross-sectional size of theduct if a constant U = 0.6 m/s velocity is to be maintained outside theboundary layer. Plot a graph of the duct size, d, as a function of x for 0 x 3 m if U is to remain constant. Assume laminar flow with boundary layerdisplacement thickness * = 1.721 (x/U)1/2, where kinematic viscosity ofair is = 1.5 x 10-3 m2/s